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A method for reparameterizing mild solutions to nonlinear evolution equations. (English) Zbl 0694.35081
Existence of solutions of evolution differential equation $$u'(t)+A(t)u(t)\ni 0$$, $$u(0)=x_ 0$$ where $$A(t)$$ is a multivalued m- accretive operator in a Banach space $$X$$ is discussed in the case when a solution to $$v'(t)+B(t)v(t)\ni 0$$, $$v(0)=x_ 0$$ is known to exist and $$A$$ and $$B$$ are related by $$A(t)=r(t)B(t)$$ with $$r(t)$$ positive and integrable.
Reviewer: S.Tersian
MSC:
 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 34G99 Differential equations in abstract spaces 35K55 Nonlinear parabolic equations
Keywords:
mild solutions; m-accretive operator
Full Text:
References:
 [1] Crandall, M.G; Evans, L.C, On the relation of the operator $$∂∂s + ∂∂τ$$ to evolution governed by accretive operators, Israel J. math., 21, 261-278, (1975) · Zbl 0351.34037 [2] Crandall, M.G; Pazy, A, Nonlinear evolution equations in Banach spaces, Israel J. math., 11, 57-94, (1972) · Zbl 0249.34049 [3] Craven, B, Lebesgue measure and integral, (1982), Pitman MA · Zbl 0491.28001 [4] Evans, L.C, Nonlinear evolution equations in an arbitrary Banach space, Israel J. math., 26, 1-42, (1977) · Zbl 0349.34043 [5] \scM. A. Freedman, Further investigation of the relation of the operator $$∂∂σ + ∂∂τ$$ to evolution governed by accretive operators, Houston J. Math., to appear. · Zbl 0811.35172
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